Question
On this coordinate plane, point B
is translated to point B′
. Which functions describe the two translations?
(1 point)
Responses
f(x)=x−5
and g(y)=y+3
f left parenthesis x right parenthesis equals x minus 5 and g left parenthesis y right parenthesis equals y plus 3
f(x)=x−6
and g(y)=y+2
f left parenthesis x right parenthesis equals x minus 6 and g left parenthesis y right parenthesis equals y plus 2
f(x)=x−2
and g(y)=y+6
f left parenthesis x right parenthesis equals x minus 2 and g left parenthesis y right parenthesis equals y plus 6
f(x)=x+6
and g(y)=y−2
is translated to point B′
. Which functions describe the two translations?
(1 point)
Responses
f(x)=x−5
and g(y)=y+3
f left parenthesis x right parenthesis equals x minus 5 and g left parenthesis y right parenthesis equals y plus 3
f(x)=x−6
and g(y)=y+2
f left parenthesis x right parenthesis equals x minus 6 and g left parenthesis y right parenthesis equals y plus 2
f(x)=x−2
and g(y)=y+6
f left parenthesis x right parenthesis equals x minus 2 and g left parenthesis y right parenthesis equals y plus 6
f(x)=x+6
and g(y)=y−2
Answers
GPT-4o mini
To determine which functions describe the translations from point B to point B′ on the coordinate plane, we need to analyze how the x-coordinate and y-coordinate of point B changes to arrive at point B′.
The translations can be expressed as:
- The x-coordinate function \( f(x) \) describes how the x-coordinate changes.
- The y-coordinate function \( g(y) \) describes how the y-coordinate changes.
To identify the correct translations, you must look for a pair of functions that represent the changes in the x and y coordinates. Here's how to evaluate the options given:
1. **f(x)=x−5 and g(y)=y+3**:
- This will move the point 5 units to the left (due to \( -5 \)) and 3 units up (due to \( +3 \)).
2. **f(x)=x−6 and g(y)=y+2**:
- This will move the point 6 units to the left and 2 units up.
3. **f(x)=x−2 and g(y)=y+6**:
- This will move the point 2 units to the left and 6 units up.
4. **f(x)=x+6 and g(y)=y−2**:
- This will move the point 6 units to the right (due to \( +6 \)) and 2 units down (due to \( -2 \)).
To select the correct translations, you would ideally need the coordinates of point B and point B′ to see exactly how they change. If you can provide those coordinates or more information about what the translations are, I would be happy to help you identify the correct functions!
The translations can be expressed as:
- The x-coordinate function \( f(x) \) describes how the x-coordinate changes.
- The y-coordinate function \( g(y) \) describes how the y-coordinate changes.
To identify the correct translations, you must look for a pair of functions that represent the changes in the x and y coordinates. Here's how to evaluate the options given:
1. **f(x)=x−5 and g(y)=y+3**:
- This will move the point 5 units to the left (due to \( -5 \)) and 3 units up (due to \( +3 \)).
2. **f(x)=x−6 and g(y)=y+2**:
- This will move the point 6 units to the left and 2 units up.
3. **f(x)=x−2 and g(y)=y+6**:
- This will move the point 2 units to the left and 6 units up.
4. **f(x)=x+6 and g(y)=y−2**:
- This will move the point 6 units to the right (due to \( +6 \)) and 2 units down (due to \( -2 \)).
To select the correct translations, you would ideally need the coordinates of point B and point B′ to see exactly how they change. If you can provide those coordinates or more information about what the translations are, I would be happy to help you identify the correct functions!